Pith. sign in

REVIEW 3 major objections 6 minor 99 references

Population statistics during search can close the loop on quantum-inspired simulated bifurcation, beating fixed schedules on most MaxCut benchmarks.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Population statistics (diversity, freeze, flip, improvement) enable closed-loop adaptive control of simulated bifurcation, yielding lowest mean gap on 74.6% of G1–G81 MaxCut graphs.

T0 review reviewed 2026-07-12 challenge →

load-bearing objection Solid engineering advance for SB solvers: closed-loop population sensing works in practice, even if the four indicators themselves were never ablated. the 3 major comments →

arxiv 2607.02540 v1 pith:GOO7LJRL submitted 2026-06-23 cs.NE

Adaptive Enhanced Quantum-inspired Simulated Bifurcation Algorithm for Population State Perception

Dongmei Liu , Jian Li , Xiubo Chen , JinTao Wang This is my paper
classification cs.NE
keywords Simulated bifurcationMaxCutAdaptive dynamicsPopulation diversityQuantum-inspired optimizationIsing modelClosed-loop control
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Simulated bifurcation solvers for combinatorial problems such as MaxCut usually run with fixed schedules for step size, coupling mode, and guidance strength. Those open-loop schedules often collapse population diversity or switch from exploration to refinement at the wrong moment. This paper argues that four simple statistics computed from the current batch of candidate solutions—symbol-space diversity, amplitude freeze rate, sign-flip activity, and recent objective improvement—are enough to sense the evolutionary stage and drive closed-loop decisions. Under that Adaptive Enhanced Quantum-inspired Simulated Bifurcation (AE-QSB) framework the authors instantiate three complementary algorithms that trade extreme-value speed against population-level refinement and density-aware generalization. On the classic G-set, the family records the lowest mean gap on roughly three-quarters of the graphs and the highest approximation ratio on more than four-fifths. The practical message is that runtime population statistics form a lightweight, computable feedback signal that lets quantum-inspired dynamics leave fixed schedules behind.

Core claim

Population statistical information collected during batch simulated-bifurcation evolution supplies a sufficient and non-redundant foundation for adaptive control, allowing quantum-inspired Ising solvers to replace fixed open-loop schedules with a closed perception–decision–execution loop and thereby improve solution quality and cross-instance robustness on MaxCut benchmarks.

What carries the argument

The four population-state indicators D (diversity), F (freeze rate), Q (flip rate) and R (improvement rate), together with the five adaptive mechanisms they drive—column-wise step size, BSB/DSB coupling selection, diversity-gated elite guidance, emergency/elite restart, and maturity-gated bit-flip plus early stopping—that close the loop inside every evaluation window.

Load-bearing premise

That the four hand-crafted indicators and their fixed decision thresholds already capture every evolutionary state that matters across graphs of widely different density and frustration, without needing per-graph retuning.

What would settle it

On a held-out suite of MaxCut instances whose density and frustration lie outside the G-set range, re-run the three AE-QSB variants with the published thresholds; if their mean-gap and approximation-ratio advantage over fixed-schedule BSB/DSB baselines disappears or reverses, the sufficiency claim for the four indicators fails.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes AE-QSB, a population-state-aware adaptive enhancement framework for quantum-inspired simulated bifurcation (SB) on Ising/MaxCut problems. It defines four runtime statistics—diversity D, freeze rate F, flip rate Q, and improvement rate R (Eqs. 7–10)—and uses them in a perception–decision–execution loop to adapt step sizes, coupling mode (BSB/DSB/mixed), elite guidance, restarts, and early stopping. Three complementary instances are introduced: ME-BSB (F-driven hard BSB→DSB switch with a weak exploration subpopulation), SE-DSB (linear mixed coupling with gated rescue), and SG-DSB (density-aware scheduling plus velocity-momentum EMA). On G22 (T=1000, B=256, 10 repeats), SE-DSB and SG-DSB report mean gaps below 0.05%; ME-BSB reports 0.26% with the best single-run time–quality trade-off. Across 71 G-set graphs, AE-QSB variants are claimed to achieve the lowest mean gap on 74.6% of graphs and the highest average approximation ratio on 84.5%. A two-tier 30-variant ablation on G22 ranks the exploration subpopulation first and rescue second, with super-additive degradation when both are removed.

Significance. If the comparative claims hold under fair experimental conditions, the work is a solid empirical methods contribution to quantum-inspired combinatorial optimization: it replaces open-loop SB schedules with a lightweight, batch-compatible closed loop driven by computable population statistics, and it documents clear complementarity among three design points (extremum-seeking, smooth refinement, density-aware generalization) on the standard G-set. Strengths include multi-metric reporting (gap, AR, TTS), Welch tests, convergence and distribution figures, and a systematic ablation that isolates super-additive exploration–rescue coupling. The framing that runtime population statistics can ground adaptive control for SB-type solvers is useful and transferable in principle to other batch Ising frameworks. The contribution is primarily empirical and engineering-oriented rather than theoretical.

major comments (3)
  1. Sec. 4.3 and Table 4: SE-DSB and SG-DSB use a multi-start strategy (3–5 independent starts for T≥250, with lexicographic selection), while Standard, GSB, Tabu, and ME-BSB are single-start. The abstract and Sec. 4.5 headline claims—lowest mean gap on 74.6% of graphs and highest AR on 84.5%—aggregate these multi-start variants with single-start baselines. This asymmetry is load-bearing for the comparative superiority claim. Either re-run all methods under matched multi-start budgets (or report single-start SE/SG only), or restate the G1–G81 win rates with multi-start clearly excluded from the primary comparison and confined to a secondary reliability analysis.
  2. Sec. 3.1 and Sec. 5.2 assert that D, F, Q, R form a “sufficient and non-redundant” state representation and that “relying on any single indicator makes it difficult to reliably distinguish evolutionary states,” yet Appendix A and Sec. 5.1 only ablate the mechanisms those indicators drive (exploration subpopulation, rescue, F-switch, density scheduling, momentum, etc.). No experiment disables or replaces subsets of the indicator set itself while holding the decision/execution layers fixed. Without such an indicator-level ablation (e.g., F+R only vs. full quartet), the central novelty claim that the four-indicator perception layer is necessary for the reported gains remains untested. A compact indicator-ablation table on G22 (and a dense/sparse pair) would close this gap.
  3. Sec. 4.1–4.2 and Algorithms 1–2 list a large free-parameter set (F_switch, β_dense, τ_min, ρ_explore, α_gbest, D_thresh, r0/κτ/κF, stall/F/Q early-stop thresholds, γ, µ bounds, rescue parameters, etc.). Sec. 5.3 acknowledges redundancy and the need for graph-feature-based auto-tuning, but the main results use fixed thresholds claimed to generalize “without per-graph retuning.” Given that the weakest assumption of the paper is precisely this fixed-threshold generalization, the manuscript should either (i) report a sensitivity study over the main thresholds on a held-out graph subset, or (ii) clearly mark which parameters were tuned on G22 versus held fixed a priori, so that the 74.6%/84.5% figures cannot be read as fully parameter-free transfer.
minor comments (6)
  1. Eq. (3): C(s) = (2W_total + s^⊤Js)/4 is standard for J=−W, but the factor of 2 vs. the usual 1/4 form should be cross-checked against the reported G22 optimum 13359 so readers can reproduce cut values from spins without ambiguity.
  2. Figure 1 is dense; the indicator→mechanism mapping box is hard to parse at print scale. Consider splitting perception vs. decision into two panels or moving the full equation block to the appendix.
  3. Notation: Table 1 lists typical values but omits several symbols used later (ρ_explore, r_t, s density scale, m momentum). A short expanded symbol table would help.
  4. Sec. 4.4: “GSB-BSB equation” appears to be a typo for GSB-BSB dynamics/collapse; please correct.
  5. References: several arXiv-style and “for review” citations (e.g., free-energy machine, edge-of-chaos SB) should be updated to final venues where available before camera-ready.
  6. Code availability is promised post-publication [50]; for reproducibility review, a frozen artifact (or anonymized repo) with seeds and G-set loaders would strengthen the empirical claims.

Circularity Check

0 steps flagged

No circularity: empirical adaptive-SB methods paper; gaps/ARs measured against external G-set optima, indicators defined from runtime stats not fitted to targets.

full rationale

AE-QSB is an engineering/methods contribution. The four indicators D, F, Q, R (Eqs. 7–10) are explicit runtime statistics of the batch population (sign diversity, amplitude freeze fraction, flip rate, recent improvement); they are not fitted to the reported MaxCut gaps or approximation ratios. Decision rules (step-size Eq. 11, mode switch Eq. 12, gated guidance Eq. 13, restarts, early stop) use hand-chosen fixed thresholds and schedules; performance is then evaluated against known external optima on the public G-set (G22 and G1–G81). Ablations (Appendix A) disable mechanisms and re-measure the same external metrics. No equation equates a claimed gap/AR to a quantity defined by the fitted parameters themselves; no uniqueness theorem or load-bearing premise is imported from overlapping-author prior work; SB dynamics and baselines (GSB, Tabu-SB, standard BSB/DSB) are external. The skeptic’s point that the indicator quartet itself is not ablated is a completeness/correctness concern, not circularity by construction. Derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

5 free parameters · 3 axioms · 2 invented entities

The central empirical claim rests on standard SB dynamics plus a large set of hand-chosen thresholds and mixing coefficients that define when and how the four indicators act. No new physical entities are postulated; the ‘invented’ objects are algorithmic constructs whose only evidence is the reported G-set performance.

free parameters (5)
  • F_switch / β_dense / τ_min (mode-switch thresholds)
    Hand-set values (e.g. F_switch≈0.23–0.24, β_dense=0.08, τ_min=0.18) that decide BSB→DSB transition; central to ME-BSB and phase-2 of SE/SG.
  • ρ_explore / ρ_late_explore (exploration subgroup fractions)
    15–18% unguided columns (later shrunk); ablation shows this is the single most important component, yet the fraction is chosen by hand.
  • α_gbest, D_thresh, ω(τ) schedule, r0/κτ/κF (guidance and mixing)
    Multiple coefficients controlling gated elite guidance strength and linear mixed coupling; density-aware s further remaps eight parameters in SG-DSB.
  • Early-stop and rescue thresholds (stall>50, F>0.98, Q<0.05, τ_resc, λ_rescue)
    Fixed numeric gates that terminate or re-anchor columns; directly affect reported TTS and final gap.
  • γ (bifurcation schedule exponent), µ0/µmin/µmax, ρR/ρF/αgap (step-size)
    Nonlinear a(t)=a(0)τ^γ and column-wise step-size formula coefficients chosen by the authors.
axioms (3)
  • domain assumption Standard supercritical-pitchfork SB continuous-time dynamics and Euler discretization (Eqs. 4–5) correctly model the search process for Ising/MaxCut instances.
    Taken from Goto et al. and used as the execution layer; no re-derivation.
  • ad hoc to paper The four statistics D, F, Q, R are complementary and jointly sufficient to distinguish exploration / transition / freeze / stagnation states for adaptive control.
    Stated in Sec. 3.1; independence is only argued constructively, not proved.
  • domain assumption G-set known optima (or best-known values) are valid external benchmarks for gap and AR.
    Standard in the MaxCut literature; used for all reported percentages.
invented entities (2)
  • AE-QSB perception–decision–execution closed loop driven by (D,F,Q,R) no independent evidence
    purpose: Replace fixed open-loop schedules with runtime population-state feedback for SB solvers.
    Core algorithmic construct of the paper; evidence is empirical performance and ablation, not independent physical measurement.
  • Three complementary algorithm instances ME-BSB, SE-DSB, SG-DSB no independent evidence
    purpose: Span the spectrum from fast extremum seeking to density-aware smooth refinement inside the AE-QSB loop.
    New named solvers; value demonstrated only on the reported G-set experiments.

reviewed 2026-07-12 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Adaptive Enhanced Quantum-inspired Simulated Bifurcation Algorithm for Population State Perception." pith.science (2026). https://pith.science/paper/GOO7LJRL

@misc{pith2026260702540,
  author       = {Pith},
  title        = {Pith review of: Adaptive Enhanced Quantum-inspired Simulated Bifurcation Algorithm for Population State Perception},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GOO7LJRL}},
  note         = {Machine review of arXiv:2607.02540}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Existing quantum-inspired simulated bifurcation algorithms rely on dynamic scheduling methods but lack the ability to adapt effectively to different problem instances. Additionally, during the evolutionary stage, balancing exploration and exploitation remains challenging. The fundamental issue stems from the widespread use of static preset parameters and globally uniform strategies, which can diminish algorithm effectiveness and lead to result homogenization. This article proposes an Adaptive Enhanced Quantum-inspired Simulated Bifurcation (AE-QSB) framework driven by population states. By leveraging perception indicators of four distinct population states, the QSB algorithm establishes a closed-loop strategy encompassing perception, decision-making, and execution. Within this framework, we introduce three complementary algorithms spanning a spectrum from efficient extremum seeking (ME-BSB), through population-level uniform refinement (SE-DSB), to density-aware adaptive scheduling (SG-DSB). On the medium-sized graph G22, both SE-DSB and SG-DSB achieve a mean gap below 0.05\%, while ME-BSB attains the optimal trade-off between runtime and solution quality with a gap of 0.26\% and the shortest single-run time. We compared AE-QSB variants with other algorithms across all benchmark graphs from G1 to G81. The results demonstrate that AE-QSB achieved the lowest mean gap on 74.6\% of the graphs and the highest average approximation rate on 84.5\% of the graphs. Ablation experiments further revealed that subgroup exploration and rescue mechanisms play crucial roles in both multifactor and single-factor components. This study demonstrates that population statistical information during dynamic evolution provides a computable and effective foundation for adaptive control, enabling quantum-inspired optimization methods to transition from fixed scheduling to data-driven closed-loop control.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

99 extracted references · 4 canonical work pages · 2 internal anchors

  1. [1]

    Frontiers in Physics , volume =

    Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer , author =. Frontiers in Physics , volume =

  2. [2]

    Enhanced Open-Source Scatter Search Algorithm for Solving

  3. [3]

    IEEE Transactions on Evolutionary Computation , pages =

    An Evolutionary Ising Optimization Framework for Unconstrained Binary Quadratic Programming , author =. IEEE Transactions on Evolutionary Computation , pages =. doi:10.1109/TEVC.2025.3566963 , copyright =

    work page doi:10.1109/tevc.2025.3566963 2025

  4. [4]

    and Vigerske, Stefan and Wiegele, Angelika , year = 2019, journal =

    Furini, Fabio and Traversi, Emiliano and Belotti, Pietro and Frangioni, Antonio and Gleixner, Ambros and Gould, Nick and Liberti, Leo and Lodi, Andrea and Misener, Ruth and Mittelmann, Hans and Sahinidis, Nikolaos V. and Vigerske, Stefan and Wiegele, Angelika , year = 2019, journal =

    2019

  5. [5]

    Brute-Forcing Spin-Glass Problems with

    Ja. Brute-Forcing Spin-Glass Problems with. Computer Physics Communications , volume =

  6. [6]

    Jiang, Yutong and Ge, Hangyu and Wang, Bi-Ying and Yuan, Shuai S. A. and Pan, Shi-Jie and Xu, Hongjing and Cui, Xiaopeng and Yung, Man-Hong and Liu, Feng and Sha, Wei E. I. , year = 2025, number =. Quantum-Inspired Beamforming Optimization for Quantized Phase-Only Massive. doi:10.48550/arXiv.2409.19938 , archiveprefix =. 2409.19938 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2409.19938 2025

  7. [7]

    Quantum-Inspired Generic Optimization for Multiuser Fluid-

    Ji, Niancong and Zheng, Gan , year = 2026, journal =. Quantum-Inspired Generic Optimization for Multiuser Fluid-. doi:10.1109/JSTSP.2026.3675440 , copyright =

    work page doi:10.1109/jstsp.2026.3675440 2026

  8. [8]

    Benchmarks for Digital Annealer with Quadratic Constrained Binary Optimization Problems , booktitle =

    Kameyama, Hiroaki and Takita, Yutaka and Parizy, Matthieu and Sazawa, Shinichi and Caballero, Pablo , year = 2024, pages =. Benchmarks for Digital Annealer with Quadratic Constrained Binary Optimization Problems , booktitle =. doi:10.1145/3638530.3664114 , isbn =

    doi:10.1145/3638530.3664114 2024

  9. [9]

    Learn from Global Correlations:

  10. [10]

    Mean Field Approximation for solving QUBO problems

    Veszeli, M. Mean Field Approximation for Solving. doi:10.48550/arXiv.2106.03238 , archiveprefix =. 2106.03238 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2106.03238

  11. [11]

    Computing and Software for Big Science , volume =

    Quantum-Annealing-Inspired Algorithms for Track Reconstruction at High-Energy Colliders , author =. Computing and Software for Big Science , volume =

  12. [12]

    Yamaoka and others , title =

    M. Yamaoka and others , title =. IEEE J. Solid-State Circuits , year =

  13. [13]

    Yamamoto and others , title =

    Y. Yamamoto and others , title =. Appl. Phys. Lett. , year =

  14. [14]

    Science Advances , volume =

    Experimental Investigation of Performance Differences between Coherent Ising Machines and a Quantum Annealer , author =. Science Advances , volume =

  15. [15]

    Goto , title =

    H. Goto , title =. Sci. Rep. , year =

  16. [16]

    Science Advances , volume =

    Combinatorial Optimization by Simulating Adiabatic Bifurcations in Nonlinear Hamiltonian Systems , author =. Science Advances , volume =

  17. [17]

    C. C. McGeoch , title =

  18. [18]

    P. L. McMahon and others , title =. Science , year =

  19. [19]

    Inagaki and others , title =

    T. Inagaki and others , title =. Science , year =

  20. [20]

    Honjo and others , title =

    T. Honjo and others , title =. Sci. Adv. , year =

  21. [21]

    Goto and K

    H. Goto and K. Endo and M. Suzuki and Y. Sakai and T. Kanao and Y. Hamakawa and R. Hidaka and M. Yamasaki and K. Tatsumura , title =. Sci. Adv. , year =

  22. [22]

    Tatsumura and A

    K. Tatsumura and A. R. Dixon and H. Goto , title =. Proc. 29th Int. Conf. Field Program. Logic Appl. (FPL) , publisher =. 2019 , pages =

    2019

  23. [23]

    Large-Scale Combinatorial Optimization in Real-Time Systems by

    Tatsumura, Kosuke , year = 2021, pages =. Large-Scale Combinatorial Optimization in Real-Time Systems by. Proceedings of the 11th. doi:10.1145/3468044.3468045 , isbn =

    doi:10.1145/3468044.3468045 2021

  24. [24]

    Tatsumura and M

    K. Tatsumura and M. Yamasaki and H. Goto , title =. Nat. Electron. , year =

  25. [25]

    A High-Performance Stochastic Simulated Bifurcation Ising Machine , booktitle =

    Zhang, Tingting and Zhang, Hongqiao and Yu, Zhengkun and Liu, Siting and Han, Jie , year = 2024, pages =. A High-Performance Stochastic Simulated Bifurcation Ising Machine , booktitle =. doi:10.1145/3649329.3655927 , isbn =

    doi:10.1145/3649329.3655927 2024

  26. [26]

    Zhang and J

    T. Zhang and J. Han , title =. IEEE Trans. Nanotechnol. , year =

  27. [27]

    Zeng and others , title =

    Q.-G. Zeng and others , title =. Commun. Phys. , year =

  28. [28]

    Tatsumura and R

    K. Tatsumura and R. Hidaka and M. Yamasaki and Y. Sakai and H. Goto , title =. IEEE Trans. Comput. Soc. Syst. , year =

  29. [29]

    Volpe and others , title =

    D. Volpe and others , title =. ACM Trans. Quantum Comput. , year =

  30. [30]

    Physical Review Letters , volume =

    Destabilization of Local Minima in Analog Spin Systems by Correction of Amplitude Heterogeneity , author =. Physical Review Letters , volume =

  31. [31]

    Communications Physics , volume =

    Scaling Advantage of Chaotic Amplitude Control for High-Performance Combinatorial Optimization , author =. Communications Physics , volume =

  32. [32]

    Communications Physics , volume =

    Simulated Bifurcation Assisted by Thermal Fluctuation , author =. Communications Physics , volume =

  33. [33]

    Physical Review Applied , volume =

    edge-of-Chaos-Enhanced Quantum-Inspired Algorithm for Combinatorial Optimization , author =. Physical Review Applied , volume =

  34. [34]

    Lee and S

    K. Lee and S. Chowdhury and K. Y. Camsari , title =. Commun. Phys. , year =

  35. [35]

    Nature Communications , volume =

    Bifurcation Behaviors Shape How Continuous Physical Dynamics Solves Discrete Ising Optimization , author =. Nature Communications , volume =

  36. [36]

    Physical Review Applied , volume =

    globally Guided Simulated Bifurcation for Enhanced Optimization , author =. Physical Review Applied , volume =

  37. [37]

    Communications Physics , volume =

    tabu-Enhanced Simulated Bifurcation for Combinatorial Optimization , author =. Communications Physics , volume =

  38. [39]

    2025 , journal =

    Variational Quantum Eigensolver with Linear Depth Problem-Inspired Ansatz for Solving Portfolio Optimization in Finance , author =. 2025 , journal =

    2025

  39. [40]

    2025 , journal =

    Next-Generation Graph Computing with Electric Current-Based and Quantum-Inspired Approaches , author =. 2025 , journal =

    2025

  40. [41]

    2025 , journal =

    Quantum-Annealing-Inspired Algorithms for Multijet Clustering , author =. 2025 , journal =

    2025

  41. [42]

    2026 , eprint =

    Simulated Bifurcation Quantum Annealing , author =. 2026 , eprint =

    2026

  42. [43]

    King, A. D. and Bernoudy, W. and King, J. and Berkley, A. J. and Lanting, T. , year =. 1806.08422 , archiveprefix =

    Pith/arXiv arXiv

  43. [44]

    Gunathilaka, M. D. S. H. and Inui, Y. and Kako, S. and Yamamoto, Y. and Aonishi, T. , year =. Mean-Field Coherent. J. Appl. Phys. , volume =

  44. [45]

    2022 , journal =

    Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing , author =. 2022 , journal =

    2022

  45. [46]

    Tiunov, E. S. and Ulanov, A. E. and Lvovsky, A. I. , year =. Annealing by Simulating the Coherent. Opt. Express , volume =

  46. [47]

    and Jeong, Y

    Rah, Y. and Jeong, Y. and Han, S. and Yu, K. , year =. Low Power Coherent. Phys. Rev. Lett. , volume =

  47. [48]

    2024 , journal =

    A Benchmarking Study of Quantum Algorithms for Combinatorial Optimization , author =. 2024 , journal =

    2024

  48. [49]

    Understanding Dynamics of Coherent

    B. Understanding Dynamics of Coherent. 2018 , journal =

    2018

  49. [50]

    Adaptive-Enhanced

    Liu, Dongmei and Li, Jian and Chen, Xiubo and Wang, Juntao , year = 2026, howpublished =. Adaptive-Enhanced

    2026

  50. [51]

    Quantum-inspired generic optimization for multiuser fluid- MIMO communications and sensing: Joint port selection and beamforming

    Ji N, Zheng G. Quantum-inspired generic optimization for multiuser fluid- MIMO communications and sensing: Joint port selection and beamforming. IEEE Journal of Selected Topics in Signal Processing, 2026, pages 1--15

    2026

  51. [52]

    Quantum-inspired beamforming optimization for quantized phase-only massive MIMO arrays, 2025

    Jiang Y, Ge H, Wang B Y, et al. Quantum-inspired beamforming optimization for quantized phase-only massive MIMO arrays, 2025

    2025

  52. [53]

    Variational quantum eigensolver with linear depth problem-inspired ansatz for solving portfolio optimization in finance

    Wang S, et al. Variational quantum eigensolver with linear depth problem-inspired ansatz for solving portfolio optimization in finance. Sci. China Inf. Sci., 2025, 68: 180504

    2025

  53. [54]

    Next-generation graph computing with electric current-based and quantum-inspired approaches

    Jang Y H, Han J, Lee S H, et al. Next-generation graph computing with electric current-based and quantum-inspired approaches. Nat. Commun., 2025, 16: 8029

    2025

  54. [55]

    Quantum-annealing-inspired algorithms for multijet clustering

    Okawa H, Tao X Z, Zeng Q G, et al. Quantum-annealing-inspired algorithms for multijet clustering. Phys. Lett. B, 2025, 864: 139393

    2025

  55. [56]

    Quantum-annealing-inspired algorithms for track reconstruction at high-energy colliders

    Okawa H, Zeng Q G, Tao X Z, et al. Quantum-annealing-inspired algorithms for track reconstruction at high-energy colliders. Computing and Software for Big Science, 2024, 8: 16

    2024

  56. [57]

    QPLIB : A library of quadratic programming instances

    Furini F, Traversi E, Belotti P, et al. QPLIB : A library of quadratic programming instances. Mathematical Programming Computation, 2019, 11: 237--265

    2019

  57. [58]

    Physics-inspired optimization for quadratic unconstrained problems using a digital annealer

    Aramon M, Rosenberg G, Valiante E, et al. Physics-inspired optimization for quadratic unconstrained problems using a digital annealer. Frontiers in Physics, 2019, 7: 48

    2019

  58. [59]

    Enhanced open-source scatter search algorithm for solving QUBO problems

    Liu D, Yang W, Wang H, et al. Enhanced open-source scatter search algorithm for solving QUBO problems. 2025

    2025

  59. [60]

    Benchmarks for digital annealer with quadratic constrained binary optimization problems

    Kameyama H, Takita Y, Parizy M, et al. Benchmarks for digital annealer with quadratic constrained binary optimization problems. In: Proceedings of Proceedings of the Genetic and Evolutionary Computation Conference Companion , Melbourne VIC Australia: ACM, 2024. 1954--1957

    2024

  60. [61]

    Simulated bifurcation quantum annealing, 2026

    Paw owski J, Tarasiuk P, Tuziemski J, et al. Simulated bifurcation quantum annealing, 2026

    2026

  61. [62]

    NMFA : Emulating the Coherent Ising Machine with a Mean-Field Algorithm , 2018

    King A D, Bernoudy W, King J, et al. NMFA : Emulating the Coherent Ising Machine with a Mean-Field Algorithm , 2018

    2018

  62. [63]

    Mean field approximation for solving QUBO problems, 2021

    Veszeli M T, Vattay G. Mean field approximation for solving QUBO problems, 2021

    2021

  63. [64]

    Mean-field coherent Ising machines with artificial Zeeman terms

    Gunathilaka M D S H, Inui Y, Kako S, et al. Mean-field coherent Ising machines with artificial Zeeman terms. J. Appl. Phys., 2023, 134: 234901

    2023

  64. [65]

    Quadratic unconstrained binary optimisation via quantum-inspired annealing

    Bowles J, Dauphin A, Huembeli P, et al. Quadratic unconstrained binary optimisation via quantum-inspired annealing. Phys. Rev. Appl., 2022, 18: 034016

    2022

  65. [66]

    Annealing by simulating the coherent Ising machine

    Tiunov E S, Ulanov A E, Lvovsky A I. Annealing by simulating the coherent Ising machine. Opt. Express, 2019, 27: 10288

    2019

  66. [67]

    Low power coherent Ising machine based on mechanical Kerr nonlinearity

    Rah Y, Jeong Y, Han S, et al. Low power coherent Ising machine based on mechanical Kerr nonlinearity. Phys. Rev. Lett., 2023, 130: 073802

    2023

  67. [68]

    A benchmarking study of quantum algorithms for combinatorial optimization

    Sankar K, et al. A benchmarking study of quantum algorithms for combinatorial optimization. Npj Quantum Inf., 2024, 10: 64

    2024

  68. [69]

    Coherent Ising machines---quantum optics and neural network perspectives

    Yamamoto Y, et al. Coherent Ising machines---quantum optics and neural network perspectives. Appl. Phys. Lett., 2020, 117: 160501

    2020

  69. [70]

    Experimental investigation of performance differences between coherent ising machines and a quantum annealer

    Hamerly R, Inagaki T, McMahon P L, et al. Experimental investigation of performance differences between coherent ising machines and a quantum annealer. Science Advances, 2019, 5: eaau0823

    2019

  70. [71]

    Understanding dynamics of coherent Ising machines through simulation of large-scale 2D Ising models

    B \"o hm F, Inagaki T, Inaba K, et al. Understanding dynamics of coherent Ising machines through simulation of large-scale 2D Ising models. Nat. Commun., 2018, 9: 5020

    2018

  71. [72]

    Brute-forcing spin-glass problems with CUDA

    Ja owiecki K, Rams M M, Gardas B. Brute-forcing spin-glass problems with CUDA . Computer Physics Communications, 2021, 260: 107728

    2021

  72. [73]

    A guide to the G -set benchmark for maximum cut

    McGeoch C C. A guide to the G -set benchmark for maximum cut. Technical report, D-Wave Systems, 2019

    2019

  73. [74]

    A fully programmable 100-spin coherent Ising machine with all-to-all connections

    McMahon P L, et al. A fully programmable 100-spin coherent Ising machine with all-to-all connections. Science, 2016, 354: 614--617

    2016

  74. [75]

    A coherent Ising machine for 2000-node optimization problems

    Inagaki T, et al. A coherent Ising machine for 2000-node optimization problems. Science, 2016, 354: 603--606

    2000

  75. [76]

    100,000-spin coherent Ising machine

    Honjo T, et al. 100,000-spin coherent Ising machine. Sci. Adv., 2021, 7: eabh0952

    2021

  76. [77]

    A 20k-spin Ising chip to solve combinatorial optimization problems with CMOS annealing

    Yamaoka M, et al. A 20k-spin Ising chip to solve combinatorial optimization problems with CMOS annealing. IEEE J. Solid-State Circuits, 2016, 51: 303--309

    2016

  77. [78]

    Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

    Goto H. Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network. Sci. Rep., 2016, 6: 21686

    2016

  78. [79]

    Combinatorial optimization by simulating adiabatic bifurcations in nonlinear hamiltonian systems

    Goto H, Tatsumura K, Dixon A R. Combinatorial optimization by simulating adiabatic bifurcations in nonlinear hamiltonian systems. Science Advances, 2019, 5: eaav2372

    2019

  79. [80]

    FPGA -based simulated bifurcation machine

    Tatsumura K, Dixon A R, Goto H. FPGA -based simulated bifurcation machine. In: Proceedings of Proc. 29th Int. Conf. Field Program. Logic Appl. (FPL). IEEE, 2019. 59--66

    2019

  80. [81]

    Large-scale combinatorial optimization in real-time systems by FPGA-based accelerators for simulated bifurcation

    Tatsumura K. Large-scale combinatorial optimization in real-time systems by FPGA-based accelerators for simulated bifurcation. In: Proceedings of Proceedings of the 11th International Symposium on Highly Efficient Accelerators and Reconfigurable Technologies , Online Germany: ACM, 2021. 1--6

    2021

Showing first 80 references.

This paper was first reviewed by grok-4.5 on July 12, 2026.